Logarithmic vector fields for quasihomogeneous curve configurations in P^2
Algebraic Geometry
2014-07-14 v1
Abstract
Let A be a union of smooth plane curves C_i, such that each singular point of A is quasihomogeneous. We prove that if C is a smooth curve such that each singular point of A U C is also quasihomogeneous, then there is an elementary modification of rank two bundles, which relates the O_{P^2} module Der(log A) of vector fields on P^2 tangent to A to the module Der(log A U C). This yields an inductive tool for studying the splitting of the bundles Der(log A) and Der(log A U C), depending on the geometry of the divisor A|_C on C.
Cite
@article{arxiv.1407.3237,
title = {Logarithmic vector fields for quasihomogeneous curve configurations in P^2},
author = {Hal Schenck and Hiroaki Terao and Masahiko Yoshinaga},
journal= {arXiv preprint arXiv:1407.3237},
year = {2014}
}
Comments
10 pages 2 figures